And now … as Monty Python would say … and now for something completely different.
This post is for all my mathematical friends. Recently it took my fancy to consider the credibility of photographs from a mathematical perspective. I wondered if I could posit a basic theoretical formula to quantify the relationship between the presented image and the original photograph?
Of course it would be quite difficult to establish reliable figures to plug into this calculation. At present such figures would be as subjective  as the opinions of the distributors and consumers of the images themselves. Even so, it may be useful to consider these relationships in a formulaic manner.
Such a theoretical formula would be based on the descriptions of the elements affecting the veracity of images, which I group into three main types:
– local manipulations (airbrushing, cloning, etc),
– global manipulations (colour adjustments, levels, etc.) and
– artifacts (compression blocking effects, etc.)
Using these elements to mathematically describe the ratio of credibility for a presented photograph in comparison with its original (pre-edited) state, could look like this:
Presentation image 1 – ∑ l,g,a
—————————– = ——————-
Original image 1
l = local manipulations
g = global manipulations
a = artifacts such as compression, display resolution
This formula can be further expanded if we consider the elements of Metadata, Context, and Photographer’s Reputation. If we assume that the metadata of the image is informative and has not been tampered with, then metadata will always add to the credibility of an image. Context and Photographer’s Reputation are elements that may add or detract from the credibility and authenticity of the image. Thus
Presentation image 1 – ∑ l,g,a
—————————– = ——————– + M ± C ± P
Original image 1
M = in camera metadata and user-entered metadata
C = context in which the image is presented
P = photographer’s reputation
M is the metadata of the image provided by technological means (metadata recorded by the camera at the time of the photograph). Metadata, assuming it is untampered itself, will always add to the authenticity of the image by providing a range of important data about the image capture such as date, time, location, camera details etc. It is also information added by the photographer post image production.
C is a quantity that can be a positive number, thus increasing image credibility, if the context in which an image is presented is supportive of the truth of the image, in which case the value of the Presentation image over the Original image could be considerably higher. Equally, it could be a negative figure, if the contextual elements within which an image is presented are false or misleading, in which case the value of the Presentation image over the Original image could be a negative figure, indicating that the Presentation image is worth less in representing reality than the Original image.
P Like Context, a Photographer’s reputation can be additive or subtractive. A photographer with a known reputation for manipulation of images should be considered more likely to manipulate the image under examination, and by the same token an image by a photographer with a reputation for not manipulating images or clearly describing any manipulations can be viewed with more surety of credibility.
Note that the idea of an image being created using staging, like the Cottingley fairies, and thus misrepresenting reality is quite relevant to the credibility of the image, however it is outside the scope of this formula for two reasons. First, other than through notation in metadata or context, there is no way to incorporate the alterations made to the actual scene being photographed. The baseline for the original photo (and thus the formula) is set at the control point of the image being recorded by the camera sensor. More importantly, one could argue that even though the scene was staged, it is in fact the real scene recorded by the sensor of the camera, staging and all.
This formula also does not take into account the way in which we as humans perceive either the original or the presentation images, which is an important second part of the two way communication of information that is representative photography, but that’s a subject for another day.
So, over to you my math friends, I would love to hear your ideas!
 However there is the possibility that in future my formula can be populated with at least some real numbers; recently such quantification was attempted in respect of image manipulation of models to create a meaningful metric of photo retouching based on geometric and photometric changes:
Kee, E., & Farid, H. (2011). A perceptual metric for photo retouching. Proceedings of the National Academy of Sciences of the United States of America, 108(50), 19907-19912.